154 cm and 168 cm b 147 cm and 175 cm 34 Empirical Rule The authors Generac

154 cm and 168 cm b 147 cm and 175 cm 34 empirical

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154 cm and 168 cm? b. 147 cm and 175 cm? 34. Empirical Rule The author’s Generac generator produces voltage amounts with a mean of 125.0 volts and a standard deviation of 0.3 volt, and the voltages have a bell-shaped distri- bution. Using the empirical rule, what is the approximate percentage of voltage amounts between a. 124.4 volts and 125.6 volts? b. 124.1 volts and 125.9 volts? 35. Chebyshev’s Theorem Heights of women have a bell-shaped distribution with a mean of 161 cm and a standard deviation of 7 cm. Using Chebyshev’s theorem, what do we know about the percentage of women with heights that are within 2 standard deviations of the mean? What are the minimum and maximum heights that are within 2 standard deviations of the mean? 36. Chebyshev’s Theorem The author’s Generac generator produces voltage amounts with a mean of 125.0 volts and a standard deviation of 0.3 volt. Using Chebyshev’s theorem, what do we know about the percentage of voltage amounts that are within 3 standard devia- tions of the mean? What are the minimum and maximum voltage amounts that are within 3 standard deviations of the mean? Beyond the Basics 37. Why Divide by Let a population consist of the values 1, 3, 14. (These are the same values used in Example 1, and they are the numbers of military intelligence satellites owned by India, Japan, and Russia.) Assume that samples of 2 values are randomly selected with replacement from this population. (That is, a selected value is replaced before the second selection is made.) a. Find the variance of the population {1, 3, 14}. b. After listing the 9 different possible samples of 2 values selected with replacement, find the sample variance (which includes division by ) for each of them, then find the mean of the sample variances . c. For each of the 9 different possible samples of 2 values selected with replacement, find the variance by treating each sample as if it is a population (using the formula for population vari- ance, which includes division by n ), then find the mean of those population variances. s 2 n - 1 s 2 s 2 > n 1? 3-3 continued
d. Which approach results in values that are better estimates of part (b) or part (c)? Why? When computing variances of samples, should you use division by n or e. The preceding parts show that is an unbiased estimator of Is s an unbiased estimator of 38. Mean Absolute Deviation Let a population consist of the values of 1, 3, and 14. (These are the same values used in Example 1, and they are the numbers of military intelligence satellites owned by India, Japan, and Russia.) Show that when samples of size 2 are randomly selected with replacement, the samples have mean absolute deviations that do not center about the value of the mean absolute deviation of the population. > s ? s 2 . s 2 n - 1? s 2 : 114 Chapter 3 Statistics for Describing, Exploring, and Comparing Data Measures of Relative Standing and Boxplots Key Concept In this section we introduce measures of relative standing, which are numbers showing the location of data values relative to the other values within a data set. The most important concept in this section is the

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